Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20295434 | C2 | semidirect |
| 3. #20295432 | C2 | semidirect |
| 4. #20295430 | C2 | semidirect |
| 5. #20295428 | C2 | semidirect |
| 6. #20295427 | C2 | semidirect |
| 11. #500×C109 | C2 | semidirect |
| 42. #13182012 | Q8 | semidirect |
| 45. C8×D109 | Q8 | semidirect |
| 108. C109 | #3164 | semidirect |
| 113. #500 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295653 | 2 |
| #20295434 | 2 |
| #20295432 | 2 |
| #20295430 | 2 |
| #20295428 | 2 |
| #20295427 | 2 |
| #20295067 | 2 |
| #20295063 | 2 |
| #107×D109 | 2 |
| #20294980 | 2 |
| #500×C109 | 2 |
| #3164 | 109 |